Simplify; express your answer in exponential form. Assume $p\neq 0, r\neq 0$. $\dfrac{{(p^{-1})^{-5}}}{{(pr^{-2})^{4}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${p^{-1}}$ to the exponent ${-5}$ . Now ${-1 \times -5 = 5}$ , so ${(p^{-1})^{-5} = p^{5}}$ In the denominator, we can use the distributive property of exponents. ${(pr^{-2})^{4} = (p)^{4}(r^{-2})^{4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(p^{-1})^{-5}}}{{(pr^{-2})^{4}}} = \dfrac{{p^{5}}}{{p^{4}r^{-8}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{5}}}{{p^{4}r^{-8}}} = \dfrac{{p^{5}}}{{p^{4}}} \cdot \dfrac{{1}}{{r^{-8}}} = p^{{5} - {4}} \cdot r^{- {(-8)}} = pr^{8}$.